On estimates of tbe solutions of systems of differential equations of the accumulation of disturbances and the stability of motion over a finite time interval

1959 ◽  
Vol 23 (4) ◽  
pp. 920-933 ◽  
Author(s):  
Chzhan Sy-In
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Stability Of Motion ◽  
Systems Of Differential Equations ◽  
The Stability

STABILITY ANALYSIS OF DIFFERENTIAL EQUATIONS WITH TIME-DEPENDENT DELAY

2006 ◽  
Vol 16 (02) ◽  
pp. 465-472 ◽  
Author(s):  
WEIHUA DENG ◽  
YUJIANG WU ◽  
CHANGPIN LI
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Finite Time ◽  
Time Dependent ◽  
Time Interval ◽  
Finite Time Interval ◽  
Predator Prey ◽  
Gauss Type ◽  
Predator Prey Models ◽  
The Stability

In this Letter, we study the stability of differential equations with time-dependent delay. Several theorems are established for stability on a finite time interval, called "interval stability" for simplicity, and Liapunov stability. These theorems are applied to the generalized Gauss-type predator–prey models, and satisfactory results are obtained.

scholarly journals Regularization of inclusions of differential equations solutions based on the kinematics of a vector field in stability problems

2021 ◽  
Vol 2099 (1) ◽  
pp. 012045
Author(s):  
A N Rogalev
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
Solution Sets ◽  
Strong Growth ◽  
System Parameters ◽  
The Stability

Abstract This paper presents the new results of computing the inclusions of sets of solutions of ordinary differential equations corresponding to perturbations acting on the solutions of the system. The regularization of algorithms for the inclusion of solutions is investigated. Inclusions of solutions are used to study the stability over a finite time interval under perturbations of the system parameters. The boundaries of solutions sets using methods that construct symbolic formulas that characterize the behavior of the system are computed. In this case, the Influence of permanent disturbances on the solutions is taken into account. It is proposed to use the parameters of the vector field of the problem in order to compensate for a strong growth of the computable solution boundaries, which is often encountered in many methods. This means the regularization of the problem of estimating inclusions of solution sets.

A method for approximating the probability functions of a Markov chain

1988 ◽  
Vol 25 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Keith N. Crank
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Finite Number ◽  
Continuous Time ◽  
Finite Time ◽  
The State ◽  
Time Interval ◽  
Continuous Time Markov Chain ◽  
Finite Time Interval ◽  
System Of Differential Equations

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

Bounded solutions for general time interval BSDEs with quadratic growth coefficients and stochastic conditions

2018 ◽  
Vol 18 (05) ◽  
pp. 1850034
Author(s):  
Huan-Huan Luo ◽  
Sheng-Jun Fan
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Quadratic Growth ◽  
Time Interval ◽  
Finite Time Interval ◽  
Bounded Solutions ◽  
One Dimensional ◽  
Stochastic Conditions ◽  
New Ideas ◽  
General Time

This paper deals with bounded solutions for general time interval one-dimensional backward stochastic differential equations (BSDEs for short) with quadratic growth coefficients and stochastic conditions. Several general results of existence, uniqueness, stability and comparison for the bounded solutions are put forward and established, which improve considerably some existing works, even though for the case of finite time interval. Some new ideas are also developed to establish these results.

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